Figure 9.4:
Typical curves indicating the real and imaginary parts of
for an atom with three visible resonances. Note
the regions of anomalous (descending) real dispersion in the
immediate vicinity of the resonances, separated by large regions
of normal (ascending) dispersion.

The are typically small compared to the oscillator frequencies
. (Just to give you an idea,
sec to
sec for optical transitions in atoms, with
similar proportionalities for the other relevant transitions.) That means
that at most frequencies,
is nearly real

Suppose we only have a few frequencies. Below the smallest , all
the (real) terms in the sum are positive and Re
. As we
increase , one by one the terms in the sum become negative (in their
real part) until beyond the highest frequency the entire sum and hence Re
.

As we sweep past each ``pole'' (where the real part in the denominator of a
single term is zero) that term increases rapidly in the real part, then
dives through zero to become large and negative, then increases monotonically
to zero. Meanwhile, its (usually small) imaginary part grows, reaching a peak
just where the real part is zero (when
is pure imaginary).
In the vicinity of the pole, the contribution of this term can dominate the
rest of the sum. We define:

Normal dispersion

as strictly increasing Re
with increasing . This is the normal situation
everywhere but near a pole.

Anomalous dispersion

as decreasing Re
with increasing . This is true only near a
sufficiently strong pole (one that dominates the sum). At that point,
the imaginary part of the index of refraction becomes (relatively)
appreciable.

Resonant Absorption

occurs in the regions where Im is
large. We will parametrically describe this next.